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The Black Hole Information Paradox,The Black Hole Information Paradox,
Alive and KickingAlive and Kicking
Joseph Polchinsk...

A Brief History of the Black Hole Information Paradox:

A Brief History of the Black Hole Information Paradox:
In 1976, Stephen Hawking argued that black holes
destroy informatio...

A Brief History of the Black Hole Information Paradox:
In 1976, Stephen Hawking argued that black holes
destroy informatio...

A Brief History of the Black Hole Information Paradox:
In 1976, Stephen Hawking argued that black holes
destroy informatio...

Thought experiments have played a major role in the
discovery of the laws of physics.
Maxwell inferred the displace-
ment ...

Hawking’s thought experiment:
singularitysingularity
horizonhorizon
First, consider the
formation of a
classical black hol...

singularitysingularity
horizonhorizon
Taking into account quantum
mechanics, the spacetime
curvature near the horizon
indu...

As a result, the black hole
eventually emits all of its
energy and disappears,
leaving only the outgoing
Hawking radiation...

Hawking’s thought
experiment is to repeat this
process many times with the
same initial state, and
measure the final state...

The outcome:
First, review density matrices. A quantum mechanical
system is described by a state vector . For
example, the...

The outcome:
For the black hole thought experiment, Hawking argued
that even if the system began in a pure state , the
fin...

Some negative reactions:
• We’ve seen density matrices before, and they just
reflect our ignorance, not a fundamental prop...

Hawking’s argument:
+
The Hawking process is a
quantum effect, and
produces a superposition,
The two photons are
entangled...

Hawking’s argument:
The net result is a highly entangled state, ~
When the evaporation is completed,
the inside (primed) d...

Purity:
If the Hawking radiation is to be in a
pure state (information is not lost, but
carried away by the radiation) it
...

Remnants:
Once the black hole is Planck-sized,
we no longer know what happens.
Maybe the evaporations stops,
leaving a pur...

Going around in circles (1976-97):
Information
loss
Information carried
away by the
Hawking radiation
Remnants

In 1997, a revolution: AdS/CFT duality (Maldacena)
Duality: when two seemingly distinct systems are
actually the same, usu...

I. Quantum gravity (actually
string theory) in an anti-de
Sitter box.
II. A quantum field theory of
gauge fields, fermions...

What does this say about the information paradox?
We can consider the Hawking
experiment in an AdS box.
Since the dual qua...

The winner!
Information
loss
Information carried
away by the
Hawking radiation
Remnants
A black hole is actually dual to a...

So what is left to do?
• The answer is not fully satisfying: it appeals to
AdS/CFT duality (which is not fully proven), an...

So what is left to do?
• The answer is not fully satisfying: it appeals to
AdS/CFT duality (which is not fully proven), an...

Black hole complementarity. A proposal for a new
relativity principle (Susskind ’93).
Observer who
falls into the
black ho...

The postulates of black hole complementarity:
I. Purity: the Hawking radiation is in a pure
state.
II. No drama: an infall...

b
b’
a
b = Aa + Ba†
a = Cb + Db†
+ C’b’ + D’b’
Creation/annihilation operators:
a: Inertial observer near horizon
b: Outgo...

Consequences of Purity
Separate Hawking radiation into early
(~first 2/3) and late (last 1/3), where the
mode b is late. E...

Purity: b + bE are in a pure state.
No drama: b + b’ are in a pure state, while b itself is
in a mixed state.
EFT: These a...

So, what to give up?
Purity?
Absence of drama?
EFT outside the horizon?
Something else, like quantum mechanics for the
inf...

So, what to give up?
Purity?
I still trust AdS/CFT here.

So, what to give up?
Absence of drama?
How bad is it - what energy excitations, and how
many?
Energy is limited only by th...

• If firewalls exist, how do they form?
Many people have proposed that the black hole
interior is not as expected, mostly ...

• If firewalls exist, how do they form?
Intuition: self-entanglement of the horizon
builds up the interior spacetime. As t...

So, what to give up?
EFT outside the horizon? Need O(1) violation of locality
to extend a macroscopic distance from the ho...

Modification of quantum mechanics for the infalling
observer? Several ideas, no coherent story yet:
• Final state boundary...

Doesn’t AdS/CFT imply that QM is unmodified?
Perhaps only for the observer at the boundary

• Are there any observational effects for black holes?
The argument is consistent with the exterior being
exactly as in th...

• Are there any consequences for cosmology?
Are cosmological horizons like black hole horizons?
Is there a version of the ...

• Where is this going?
Trivial resolution? Looking unlikely.
I still trust AdS/CFT, so keep purity, but AdS/CFT may
tell u...

From G. ‘t Hooft
Another puzzling properties of black holes is that they
have a thermodynamic entropy proportional to thei...

Another version: mining the black hole:
Drop a box near to the horizon, let it fill with Unruh
(acceleration) radiation, a...

• If firewalls exist, when do they form?
Entanglement argument gives upper bound ~ (black
hole lifetime)/2, but most black...

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